Chapter 9 Review - Part II

Chapter 9 Review - Part II - Comparing Two Means Two groups...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Comparing Two Means Two groups can be compared on a response variable if we compare their . I . Confidence Intervals Let μ 1 : mean corresponding to the response variable for the first group. μ 2 : mean corresponding to the response variable for the second group. We can compare the two groups by constructing a confidence interval of the difference Step I : Assumptions : i) samples from two groups. ii) Approximate population distribution for each of the two groups. Note : This is mainly important for small sample sizes but our confidence interval would still hold if this assumption is violated even for small sample sizes.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Step II : Let us draw samples of sizes n 1 and n 2 from the two groups. Let the sample means for the two groups be and respectively (Here x-bar = ) Thus, the difference in sample means will be . Step III : As for the single mean, the confidence interval for is obtained by adding and subtracting a to its point estimate As before, the margin of error is the product of the appropriate and the of . It can be shown that the standard error of is given by s.e = where and are the of the first and second samples. Note : Always remember that for estimates calculated from samples, s.e (est 1 – est 2) =
Background image of page 2
1 -bar and est 2 is x 2 -bar, s.e (est 1) is S 1 2 /n 1 while s.e (est 2) is S 2 2 /n 2. So, for the difference of means, the margin of error will be m.e = The exact degrees of freedom of the t score is difficult to calculate*. Any statistical software will give you the value. But, if and , the df becomes . Otherwise, the degrees of freedom can be taken to be the smaller of . If we need a 95% (99%) confidence interval, t = t 0.025 (t 0.005 ) which is the t score with right tail area/probability 0.025 (0.005).
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/18/2008 for the course EXP 3116 taught by Professor Fasig during the Spring '08 term at University of Florida.

Page1 / 12

Chapter 9 Review - Part II - Comparing Two Means Two groups...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online